Question

what force is required to keep a 6x10²⁴ kg mass moving in a circle of radius 1.5x10¹¹m with a speed of 3.0x10⁴ m/s?
a 1.2x10¹⁸ n
b 3.6x10²² n
c 8.0x10⁷ n
d 7.3x10²⁶ n

Explanation:

Step1: Recall the formula for centripetal force

The formula for centripetal force is \(F = \frac{mv^{2}}{r}\), where \(m\) is the mass, \(v\) is the speed, and \(r\) is the radius.

Step2: Substitute the given values into the formula

Given \(m = 6\times10^{24}\text{ kg}\), \(v = 3.0\times 10^{4}\text{ m/s}\), and \(r=1.5\times 10^{11}\text{ m}\).
Substitute these values into \(F=\frac{mv^{2}}{r}\):

$$
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Step3: Simplify the expression

First, multiply the numerator: \((6\times 10^{24})\times(9\times 10^{8})=54\times 10^{32}\)
Then, divide by the denominator: \(\frac{54\times 10^{32}}{1.5\times 10^{11}}=\frac{54}{1.5}\times10^{32 - 11}\)
\(\frac{54}{1.5}=36\), and \(10^{32-11}=10^{21}\)
So \(F = 3.6\times 10^{22}\text{ N}\)

Answer:

B. \(3.6\times 10^{22}\text{ N}\)